In 1870 the average ground temperature in Paris was 11.8°C. Since then it has risen at a nearly constant rate, reaching 13.5°C in 1969.

(a) Express the temperature T (in °C) in terms of time t (in years), where t = 0 corresponds to the year 1870 and 0 ≤ t ≤ 99.

Question

Mathematics

Hazel Rivers

6 February, 17:33

In 1870 the average ground temperature in Paris was 11.8°C. Since then it has risen at a nearly constant rate, reaching 13.5°C in 1969.

(a) Express the temperature T (in °C) in terms of time t (in years), where t = 0 corresponds to the year 1870 and 0 ≤ t ≤ 99.

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Answers (1)

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Mathew Dickerson · Answer 1

T = T0 (r^t)

13.5 = 11.8 (r) ^99

r^99 = 13.5/11.8 = 1.144

log r^99 = log 1.144

99 log r = log 1.144

log r = log 1.144 / 99 = 0.00059

r = 10^0.00059 = 1.00136

T = 11.8 (1.00136) ^t

In 1870 the average ground temperature in Paris was 11.8°C. Since then it has risen at a nearly constant rate, reaching 13.5°C in 1969.(a) Express the temperature T (in °C) in terms of time t (in years), where t = 0 corresponds to the year 1870 and 0 ≤ t ≤ 99.

In 1870 the average ground temperature in Paris was 11.8°C. Since then it has risen at a nearly constant rate, reaching 13.5°C in 1969.

(a) Express the temperature T (in °C) in terms of time t (in years), where t = 0 corresponds to the year 1870 and 0 ≤ t ≤ 99.